Question

You win a game with probability 0.511. Each game you play is independent. If you play the game 10 times, What is the probability that you win 6 of the 10 times.

Answer 1

This is clearly a BINOMIAL EXPERIMENT, because of the following reasons.

1) Number of games played i.e number of trials =10 is fixed.

2)All the games are independent and identical in the aspect of winning.

3) Considering a game it results in two outcomes either win(success) or lose(failure).

4) Probability of winning i.e probability of success = 0.511 is same for every game.

Now let X be the number of games win out of 10 games.

Then we need to find P(X=6).

Formula:

P(X=x) = ncx . p^x . q^n-x .

Here n= 10, X= 6, p = 0.511, q=1-p=0.489

So, P(X=6) = 10c6 . (0.511)^6 . (0.489)^10-6 .

= 0.2138 answer.